Video Transition? 3 Parts of a Pic?
This is quite easy to do using the compositor.


In the UV/Image editor create a series of masks, one for each piece of the image.


In the compositor use each mask as alpha channel on the image, connect each element to a transform node and combine them using alpha over nodes.


we are going to construct the movement backwards, starting from the end of the animation. 

Move in the timeline to the frame that will be the end of the animation (where all of the elements are combined) and set a key frame for the transformation cooridinates.


In the time line go to the frame of the animation where you want the motion to start and move the values for the transformation so that each of the elements has moved away and set a keyframe.


The elements should move now to the end position.